Abstract
Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction–diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to ∞
, gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh–Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.
, gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh–Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.
| Original language | English |
|---|---|
| Article number | 39 |
| Number of pages | 35 |
| Journal | Journal of Mathematical Biology |
| Volume | 86 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 28 Jan 2023 |
Bibliographical note
Funding Information:The authors would like to thank Andrew Krause of the University of Durham for helpful remarks. EV-S has received Ph.D. funding from ANID, Beca Chile Doctorado en el extranjero, number 72210071.
Funding Information:
The authors would like to thank Andrew Krause of the University of Durham for helpful remarks. EV-S has received Ph.D. funding from ANID, Beca Chile Doctorado en el extranjero, number 72210071.
Publisher Copyright:
© 2023, The Author(s).
Structured keywords
- Engineering Mathematics Research Group
Keywords
- Reaction-diffusion
- Diffusion-driven instability
- Spatio-temporal oscillations
- Turing instability
- wave instability